Implementation:Pyro ppl Pyro AffineBeta

Knowledge Sources	Pyro Pyro Distributions
Domains	Probability_Distributions, Deep_Learning
Last Updated	2026-02-09 09:00 GMT

Overview

A Beta distribution scaled and shifted by an affine transformation, supporting bounded random variables on arbitrary intervals.

Description

The AffineBeta distribution is a TransformedDistribution that applies an affine transformation to a standard Beta distribution. Given a Beta-distributed random variable X, the AffineBeta produces Y = loc + scale * X, which has support on the interval [loc, loc + scale].

The distribution is parameterized by:

• concentration1 (alpha) -- The first concentration parameter of the underlying Beta distribution. Controls the shape near the lower bound.
• concentration0 (beta) -- The second concentration parameter of the underlying Beta distribution. Controls the shape near the upper bound.
• loc -- The location (shift) parameter, equal to the lower bound of the support.
• scale -- The scale parameter, where the upper bound equals loc + scale.

The class extends Pyro's TransformedDistribution with a Beta base distribution and an AffineTransform. It provides both sample and rsample methods, each applying the affine transform and then clamping the output to avoid numerical issues at the boundaries. The clamping uses a machine-epsilon-based buffer (eps * scale) to prevent NaN and Inf values in gradients that can occur at exact boundary values.

Key computed properties include:

• low -- The lower bound of the distribution, equal to loc.
• high -- The upper bound of the distribution, equal to loc + scale.
• sample_size -- The sum concentration1 + concentration0, representing the effective sample size of the Beta prior.
• mean -- Computed as loc + scale * Beta.mean.
• variance -- Computed as scale^2 * Beta.variance.

Usage

Use AffineBeta when you need a bounded distribution on an arbitrary interval [loc, loc + scale] rather than the standard [0, 1] interval of a Beta distribution. This is common in Bayesian models where parameters have known physical bounds, or when modeling proportions relative to a known range.

Code Reference

Source Location

• Repository: Pyro
• File: pyro/distributions/affine_beta.py

Signature

class AffineBeta(TransformedDistribution):
    arg_constraints = {
        "concentration1": constraints.positive,
        "concentration0": constraints.positive,
        "loc": constraints.real,
        "scale": constraints.positive,
    }

    def __init__(self, concentration1, concentration0, loc, scale, validate_args=None)

Import

from pyro.distributions import AffineBeta

I/O Contract

Inputs

Name	Type	Required	Description
concentration1	float or torch.Tensor	Yes	First concentration parameter (alpha) of the Beta distribution. Must be positive.
concentration0	float or torch.Tensor	Yes	Second concentration parameter (beta) of the Beta distribution. Must be positive.
loc	float or torch.Tensor	Yes	Location (shift) parameter. Defines the lower bound of the support.
scale	float or torch.Tensor	Yes	Scale parameter. Must be positive. Upper bound is loc + scale.
validate_args	bool or None	No	Whether to enable argument validation.

Outputs

Name	Type	Description
sample	torch.Tensor	Samples from the affine-transformed Beta, clamped to (low + eps, high - eps) for numerical stability.
rsample	torch.Tensor	Reparameterized samples with the same clamping behavior.
log_prob	torch.Tensor	Log probability density (inherited from TransformedDistribution).
mean	torch.Tensor	Mean of the distribution: loc + scale * alpha / (alpha + beta).
variance	torch.Tensor	Variance of the distribution: scale^2 * alpha * beta / ((alpha + beta)^2 * (alpha + beta + 1)).
low	torch.Tensor	Lower bound of the support (equals loc).
high	torch.Tensor	Upper bound of the support (equals loc + scale).
support	constraints.interval	The interval constraint [low, high].

Usage Examples

Basic Usage

import torch
from pyro.distributions import AffineBeta

# Beta distribution on [0, 10] with mode near 3
dist = AffineBeta(
    concentration1=torch.tensor(3.0),
    concentration0=torch.tensor(7.0),
    loc=torch.tensor(0.0),
    scale=torch.tensor(10.0),
)

samples = dist.sample(torch.Size([1000]))
print(samples.min().item(), samples.max().item())  # approximately 0..10

log_p = dist.log_prob(torch.tensor(3.0))
print(dist.mean)      # tensor(3.0)
print(dist.variance)  # tensor(1.9091)

Modeling Bounded Parameters

import pyro
import pyro.distributions as dist
import torch

# Temperature constrained between -40 and 50 degrees
temp = pyro.sample(
    "temperature",
    dist.AffineBeta(
        concentration1=torch.tensor(5.0),
        concentration0=torch.tensor(3.0),
        loc=torch.tensor(-40.0),
        scale=torch.tensor(90.0),  # high = -40 + 90 = 50
    ),
)

Batched Distribution

import torch
from pyro.distributions import AffineBeta

# Batch of 4 distributions with different bounds
dist = AffineBeta(
    concentration1=torch.ones(4) * 2,
    concentration0=torch.ones(4) * 2,
    loc=torch.tensor([0.0, 1.0, -1.0, 5.0]),
    scale=torch.tensor([1.0, 2.0, 3.0, 0.5]),
)

samples = dist.sample()
print(samples.shape)  # torch.Size([4])
print(dist.low)       # tensor([ 0.,  1., -1.,  5.])
print(dist.high)      # tensor([1., 3., 2., 5.5])

Related Pages

• Principle:Pyro_ppl_Pyro_Heavy_Tailed_Distributions